键结与晶体结构 Crystal Structures and Bonding in Solids

鍵結與晶體結構CrystalStructuresandBondinginSolidsSchrodingerEquation⇒structureofhydrogenatom⇒propertiesofotheratoms⇒periodictable⇒asystemofatoms,crystals⇒semiconductors⇒integratedcircuits(I.C.)•3formsorphasesofmattergasliquidcondensedsystemsolid(凝態)orderdisordersolidliquidgas•solidamorphousÆshortrangeordercrystalÆlongrangeorderglassmoleculararrangementcrystallinearrangement晶體結構(CrystalStructures)Æa3-dimensionalperiodicarrayofatomsormolecules•spacelattice–regularperiodicarrangementofpointsinspace•basis:atomorgroupofatoms•(lattice)+(basis)ÆcrystalstructureatomAatomBbasisspacelatticecrystal•only7categoriesand14possiblelatticearrangement:14Bravaislattices•NaClstructure:fcc,basisconsistsofaNaandaClatoms•CsClstructure:cubic,basisconsistsofaClandaCsatoms•Diamondstructure:fcc,basisconsistsof2identicalatoms(C,Si,Ge,Sn)離子鍵與離子晶體(IonicBondingandCrystals)•between“+”and“–”ions例:inNaClmoleculeNa+5.14eVÆNa++e-Cl+e-ÆCl-+3.62eVCoulomb’sattractionpotentialenergybetweenNa+andCl-Ep=–————=-9x10-9x(1.6x10-19)2/(2.5x10-10)=-9.18x10-19J=-5.73eV(r~2.5ÅforNaCl)netenergyreleased:E=3.62eV+5.73eV–5.14eV=4.22eVÆenergyneededtobreakapartaNaClmolecule1e24πεorCsClEx.IonicbondincrystalsNaCl•Inanioniccrystal:E=-α————r:distancebetween2nearestionsα:Madelung’sconstant1e24πεor例:NaClfcccrystal,α=1.7476,Na+has:(1)6nearestCl-ionsatrÆE6=-6(1/4πεo)(e2/r)(2)12nextnearestNa+at2rÆE12=12(1/4πεo)(e2/2r)(3)8Cl-at3rÆE8=-8(1/4πεo)(e2/3r)(4)6Na+at2rÆE6’=6(1/4πεo)(e2/2r)…..⇒Etotal=–————[6-——+——-——+…..]=-1.7476————1e24πεor12283621e24πεor•bindingenergy=½Etotal~4eV(r~2.8ÅforcrystallineNaCl)(comparetokBT=0.0259eVat300K)•ioniccrystalsareusuallyhardandhavehighmeltingpoints(e.g.801oCforNaCl,845oCforLiF)•becausetherearenofreeorlooselyboundedelectronÆinsulators例:氫分子(H2molecule)e-spendalotoftimebetween2protonsÆprotonsattractedtowardcenterandeachotherÆcovalentbond共價鍵(CovalentBond)~0.7Å•covalentbondsinsolids:diamond(C),Si,GeC:1s22s22p2Si:1s22s22p63s23p2Æneed4e-tohaveafullpsubshellGe:1s22s22p63s23p63d104s24p2⇒4covalentbondstoeachatom(tetrahedralstructure)•covalentbondsisverystrong例:7.4eVfordiamond,12.3eVforSiC(carborandum)•covalentbondingmaterialsareusuallyinsulatorsorsemiconductors金屬鍵(MetallicBond)–formedbyatomsthathaveafewweaklyboundedelectronsintheoutersubshellsÆanarrayofheavy“+”ionsina“sea”ofhighlymobileelectronsÆmobilee-providethe“glue”thatkeepsthestructuretogether分子鍵/凡得瓦鍵(MolecularorvanderWaalsBond)–fromdipole-dipoleinteraction例:H2Omolecule-++我喜歡水!我喜歡油漬!icecrystal例:forraregasatomsÆelectrondistributionissymmetriconaverageÆbutthemovementbetweenelectronsofdifferentatomstendtocoupleÆallraregases(exceptHe)condenseatsufficientlylowtemp.andformcrystals例:apolarmoleculeattractnonpolarmolecule